Finite Group Databasebeta

← #14575161

Subgroups — #14575161

Order 2432.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597395C211yesmaximal, characteristic, complemented
2C2×#10597396C211yesmaximal, characteristic, complemented
3#11927190C211yesmaximal, characteristic, complemented
4#11926936C211yesmaximal, characteristic, complemented
5#11926800C211yesmaximal, characteristic, complemented
6#11926775C211yesmaximal, characteristic, complemented
7#11926759C211yesmaximal, characteristic, complemented
8#11926746C211yesmaximal, characteristic, complemented
9#11926706C211yesmaximal, characteristic, complemented
10#11926704C211yesmaximal, characteristic, complemented
11#11926694C211yesmaximal, characteristic, complemented
12#11926689C211yesmaximal, characteristic, complemented
13#11926654C211yesmaximal, characteristic, complemented
14#11926616C211yesmaximal, characteristic, complemented
15C19×#547C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#41×C19C2211yescharacteristic, complemented
18C2×#64541C2211yescharacteristic
19C22×D76C2211yescharacteristic
20C19×C4⋊Q8C2211yescharacteristic, complemented
21C19×#123—21no—
22C19×#123—21no—
23C19×C22⋊Q8C2211yescharacteristic
24C19×C22⋊Q8C2211yescharacteristic, complemented
25C19×#121—21no—
26C4×D4×C19C2211yescharacteristic
27C4×D4×C19C2211yescharacteristic, complemented
28C2×C4⋊C4×C19—21no—
29#10597396—24no—
30#10597395—24no—
31C2×#64528C2211yescharacteristic, complemented
32C2×#64528C2211yescharacteristic, complemented
33C2×#64527C2211yescharacteristic
34C2×#64527C2211yescharacteristic
35C2×#64527C2211yescharacteristic
36C2×#64527C2211yescharacteristic
37#10597383—21no—
38C2×#64526C2211yescharacteristic, complemented
39C2×#64525C2211yescharacteristic
40C2×#64525C2211yescharacteristic
41#10597376C2211yescharacteristic
42#10597370C2211yescharacteristic
43C2×#64520C2211yescharacteristic
44C22×C19⋊C8C2211yescharacteristic, complemented
45#10597340—21no—
46#10597330—21no—
47C22⋊C4×D19—21no—
48#10597321C2211yescharacteristic
49C4×D76C2211yescharacteristic
50#10597292C2211yescharacteristic, complemented
51#10597292C2211yescharacteristic, complemented
52#10597289C2211yescharacteristic, complemented
53C22⋊(C19⋊C8)C2211yescharacteristic
54C22⋊(C19⋊C8)C2211yescharacteristic, complemented
55#10597267C2211yescharacteristic, complemented
56#10597266C2211yescharacteristic
57#10597266C2211yescharacteristic
58#10597265C2211yescharacteristic, complemented
59C4⋊(C19⋊C8)C2211yescharacteristic, complemented
60#10597260C2211yescharacteristic, complemented
61C23×D19—21no—
62#41×C19—22no—
63#41×C19—22no—
64#41×C19—41no—
65#41×C19—41no—
66C2×Q8×C19C2311yescharacteristic
67C2×Q8×C19C2311yescharacteristic
68C2×D4×C19—21no—
69C2×D4×C19—21no—
70C2×D4×C19D411yescharacteristic
71C2×D4×C19C2311yescharacteristic
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19C2311yescharacteristic
76C22×C4×C19C2311yescharacteristic
77C2×C22⋊D19—21no—
78C2×C22⋊D19—21no—
79#64541—22no—
80#64541—41no—
81C2×D76—22no—
82C2×D76—21no—
83C2×D76—41no—
84C2×D76C2311yescharacteristic
85C2×D76C2311yescharacteristic
86C2×C4×D19—21no—
87C2×C4×D19—21no—
88C2×Dic38C2311yescharacteristic
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19D411yescharacteristic
94C4⋊C4×C19C2311yescharacteristic
95C22⋊C4×C19—21no—
96C22⋊C4×C19—21no—
97C22⋊C4×C19—21no—
98C22⋊C4×C19D411yescharacteristic
99C22⋊C4×C19D411yescharacteristic
100C42×C19C2311yescharacteristic
101C22⋊Dic19—21no—
102#64528—22no—
103#64528—41no—
104#64527—22no—
105#64527—22no—
106#64527—22no—
107#64527—41no—
108#64526—22no—
109#64525—22no—
110#64525D414yescomplemented
111(C2×D19)⋊C4—21no—
112(C2×D19)⋊C4—21no—
113(C2×D19)⋊C4—21no—
114(C2×D19)⋊C4—21no—
115C4⋊Dic19C2311yescharacteristic
116Dic19⋊C4—21no—
117#64520—22no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8C2311yescharacteristic
120C2×C19⋊C8C2311yescharacteristic
121C2×C19⋊C8C2311yescharacteristic
122C2×C19⋊C8C2311yescharacteristic
123C23×C19—21no—
124C23×C19C2×D411yescharacteristic
125C23×C19C2×D411yescharacteristic
126C22×D19—21no—
127C22×D19—21no—
128C22×D19—42no—
129C22×D19—42no—
130C22×D19—81no—
131Q8×C19—21no—
132Q8×C19—21no—
133Q8×C19—21no—
134Q8×C19—21no—
135D4×C19—21no—
136D4×C19—41no—
137D4×C19—42no—
138D4×C19—42no—
139D4×C19C2×D412yes—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—42no—
150C2×C4×C19C2×D411yescharacteristic
151C2×C4×C19C2×D411yescharacteristic
152C2×C4×C19C2×D411yescharacteristic
153C2×C4×C19C2×D411yescharacteristic
154C2×C4×C19C2411yescharacteristic
155C22⋊D19—42no—
156C22⋊D19—81no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159D76—21no—
160D76—21no—
161D76—21no—
162D76—42no—
163D76C2×D412yes—
164C4×D19—42no—
165C4×D19—81no—
166Dic38—21no—
167Dic38—21no—
168C19⋊C8—21no—
169C19⋊C8—21no—
170C19⋊C8—21no—
171C19⋊C8C2×D412yes—
172#3267—191nomaximal, Sylow
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—22no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19C22×D411yescharacteristic
183C2×D19—22no—
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—41no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—84no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—41no—
195C4×C19—41no—
196C4×C19—41no—
197C4×C19C22×D411yescharacteristic
198C4×C19H(5,𝔽2)11yescharacteristic
199Dic19—41no—
200Dic19—41no—
201C2×AGL(1,ℤ/8)—191no—
202C2×#135—191no—
203#547D1911yescharacteristic, complemented
204#546—191no—
205#497—191no—
206#470—191no—
207#465—191no—
208#463—191no—
209#461—191no—
210#452—191no—
211#452—191no—
212#450—191no—
213#449—191no—
214#442—191no—
215#435—191no—
216C2×C19—41no—
217C2×C19—41no—
218C2×C19—42no—
219C2×C19D4211yescharacteristic
220C2×C19#57511yescharacteristic
221C2×C19#57711yescharacteristic
222D19—42no—
223D19—81no—
224C2×#41—191no—
225C2×#41C2×D1911yescharacteristic
226C2×#41C2×D1911yescharacteristic, complemented
227C22×D4—191no—
228AGL(1,ℤ/8)—384no—
229#135—384no—
230C2×Q16—191no—
231C2×Q16—191no—
232C2×SD16—191no—
233C2×SD16—191no—
234C2×SD16—191no—
235C2×SD16—191no—
236C2×SD16—191no—
237C2×D8—191no—
238C2×D8—191no—
239C2×M16—191no—
240C22×C8—191no—
241C4⋊Q8C2×D1911yescharacteristic, complemented
242#124—191no—
243#123—21no—
244#123—21no—
245#123—381no—
246C22⋊Q8—191no—
247C22⋊Q8C2×D1911yescharacteristic
248C22⋊Q8C2×D1911yescharacteristic, complemented
249#121—21no—
250#121—191no—
251#121—381no—
252#120—381no—
253C4×D4—191no—
254C4×D4C2×D1911yescharacteristic
255C4×D4C2×D1911yescharacteristic, complemented
256C2×C4⋊C4—21no—
257C2×C22⋊C4—381no—
258#106—191no—
259C4⋊C8—191no—
260#103—191no—
261#103—191no—
262#103—191no—
263#102—191no—
264#102—191no—
265#102—191no—
266C22⋊C8—191no—
267C22⋊C8—191no—
268#97—191no—
269C19#326711yescharacteristic, complemented, Sylow
270C24—381no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275#41—382no—
276#41—761no—
277C2×Q8—191no—
278C2×Q8C22×D1911yescharacteristic
279C2×Q8C22×D1911yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—191no—
283C2×D4—191no—
284C2×D4—382no—
285C2×D4—381no—
286C2×D4—381no—
287C2×D4—381no—
288C2×D4—761no—
289C2×D4C22⋊D1911yescharacteristic
290C2×D4C22×D1911yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4C22×D1911yescharacteristic
297C22×C4C22×D1911yescharacteristic
298Q16—382no—
299Q16—761no—
300SD16—382no—
301SD16—382no—
302SD16—382no—
303SD16—382no—
304SD16—761no—
305D8—194no—
306D8—382no—
307M16—382no—
308C2×C8—191no—
309C2×C8—191no—
310C2×C8—191no—
311C2×C8—191no—
312C2×C8—382no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—191no—
318C4⋊C4—381no—
319C4⋊C4C22⋊D1911yescharacteristic
320C4⋊C4C22×D1911yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—381no—
328C22⋊C4—381no—
329C22⋊C4C22⋊D1911yescharacteristic
330C22⋊C4C22⋊D1911yescharacteristic
331C42C22×D1911yescharacteristic
332C23—21no—
333C23—381no—
334C23—381no—
335C23—762no—
336C23—762no—
337C23—1521no—
338C23C2×C22⋊D1911yescharacteristic
339C23C2×C22⋊D1911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—381no—
345Q8—381no—
346D4—21no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—192no—
351D4—381no—
352D4—381no—
353D4—381no—
354D4—762no—
355D4—762no—
356D4—1521no—
357D4D4×D1912yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—762no—
371C2×C4—1521no—
372C2×C4C2×C22⋊D1911yescharacteristic
373C2×C4C2×C22⋊D1911yescharacteristic
374C2×C4C2×C22⋊D1911yescharacteristic
375C2×C4C2×C22⋊D1911yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C8—192no—
378C8—381no—
379C8—381no—
380C8—381no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—382no—
391C22—761no—
392C22—761no—
393C22—761no—
394C22—761no—
395C22—761no—
396C22—1524no—
397C22C22×C22⋊D1911yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—761no—
406C4—761no—
407C4C2×D4×D1911yescharacteristic
408C4#1059743011yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—762no—
413C2—1521no—
414C2D4×C22⋊D1911yescharacteristic
415C2#1192734211yescharacteristic
416C2#1192735211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#547C2
socleC22×C19C22×D4
hypercenter#547D19
hypocenterC19#3267
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10597395C2semidirect
2. C2×#10597396C2semidirect
3. #11927190C2semidirect
4. #11926936C2semidirect
5. #11926800C2semidirect
6. #11926775C2semidirect
7. #11926759C2semidirect
8. #11926746C2semidirect
9. #11926706C2semidirect
10. #11926704C2semidirect
11. #11926694C2semidirect
12. #11926689C2semidirect
13. #11926654C2semidirect
14. #11926616C2semidirect
15. C19×#547C2semidirect
17. C2×#41×C19C22semidirect
20. C19×C4⋊Q8C22semidirect
24. C19×C22⋊Q8C22semidirect
27. C4×D4×C19C22semidirect
31. C2×#64528C22semidirect
32. C2×#64528C22semidirect
38. C2×#64526C22semidirect
44. C22×C19⋊C8C22semidirect
50. #10597292C22semidirect
51. #10597292C22semidirect
52. #10597289C22semidirect
54. C22⋊(C19⋊C8)C22semidirect
55. #10597267C22semidirect
58. #10597265C22semidirect
59. C4⋊(C19⋊C8)C22semidirect
60. #10597260C22semidirect
110. #64525D4semidirect
203. #547D19semidirect
226. C2×#41C2×D19semidirect
241. C4⋊Q8C2×D19semidirect
248. C22⋊Q8C2×D19semidirect
255. C4×D4C2×D19semidirect
269. C19#3267semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#105973952
C2×#105973962
#119271902
#119269362
#119268002
#119267752
#119267592
#119267462
#119267062
#119267042
#119266942
#119266892
#119266542
#119266162
C19×#5472
#326719